WBJEE 2012 Math Solved Paper

Given 3xlogex‌

dy

dx

+y=2logex
Dividing both sides by 3x loge x, we get
‌

dy

dx

+‌

1

3xlogex

y=‌

2logex

3xlogex

⇒‌

dy

dx

+‌

1

3xlogex

y=‌

2

3x

which is linear form

dy

dx

+Py=Q, here P and Q are function of x and the integrating factor is given by the following formula e∫Pdx
∴IF=e∫‌

1

3xlogex

dx
Put logex=t⇒‌

1

x

dx=dt
=e

1

3

‌∫‌

dt

t

=e

1

3

‌log‌t
=elog‌t

1

3

=t

1

3

=(logex)

1

3